On the Study and Possible Applications of Minimally Complex Chaos

The nature of chaos is elusive and disputed, however it can be connected to sensitivity to initial conditions caused by nonlinearity of the equations describing chaotic phenomena. A nowhere-near comprehensive list of such equations can still be shown: the Boltzmann equation, Ginzburg-Landau equation, Ishimori equation, Korteweg-de Vries equation, Landau-Lifshitz-Gilbert equation, Navier-Stokes equation, and many more. This disproportionality between input and output creates an analytically-difficult situation, one that is complicated both algebraically and numerically – however, the study of equations that are both simple and chaotic may yield useful connections between algebraic complexity and chaos. Such connections can be used to determine the simplest possible chaotic function, which can be used as a “chaotic operator” for various non-chaotic or chaotic functions, thus reducing the problem of chaos to one based strictly on algebra.